一种基于Boltzmann方程的碳基复合材料氧化烧蚀微观界面的追踪方法

A Boltzmann model for calculating the microscopic ablation morphology of C/C composites

针对碳基复合材料的非均相特点,构建环境-纤维—中间相-基体多相单胞烧蚀模型,应用非平衡统计物理学的Boltzmann方程,求解该扩散—表面非均相氧化反应体系中各相的空间演化过程,实现对介尺度下烧蚀界面的精确追踪。本文先对两相单胞模型进行了求解,获得了与解析解一致的结果,验证了模型。再对三相单胞模型的烧蚀过程进行了数值模拟。结果表明,氧化烧蚀界面的形貌主要取决于相邻两相之间的状态;气相浓度的线性化假设在远离界面处具有合理性,但在界面附近气相浓度呈非线性分布。由于扩散的限制,纤维与基体之间的界面相在氧化烧蚀过程中存在最大烧蚀深度。通过数值模拟给出了烧蚀深度与舍伍德数、纤维半径和反应速率比之间的函数关系,提出的界面追踪算法在求解过程中表现出了很好的稳定性。

A two-solid-phase cell ablation model involving an oxidative gas phase,a carbon fiber and a carbon matrix is proposed and the Boltzmann equation of non-equilibrium statistical physics was numerically solved to simulate the spatial evolution of each phase at the mesoscopic scale during the diffusion-surface reaction process.The predicted results of the model are in a good agreement with those of the analytical solution.A more complex three-solid-phase cell model that considered a fiber/matrix interphase was numerically simulated.The simulation results show that the roughness of the composites after oxidative ablation mainly depends on the morphology of the interphase between the fiber and the matrix.The hypothesis of a linear distribution of the concentrations of gas species is reasonable only away from the interphase,but not near the interphase.A maximum ablation depth exists due to diffusion limitation near the fiber/matrix interphase,which depends on parameters such as the Sherwood number,the fiber radius and the reaction rate ratio of the fiber to the interphase with the oxidative gas.This interphase tracking algorithm has good stability during numerical calculations.